After seeing the suggestions about sport/exercise which are less stressful, or even good for my knees, I chose squatting. From the suggestions, it can be done with minimal space and equipment at my home, which is also a plus. Especially I would try squatting with my own body weight so as not to give extra pressure on the knees. (Anyway I don't have a barbell.)

But Ryan Miller stated that "If you decide to try squats, just make sure your knees do not go more forward than your toes at the bottom of the squat."

I tried to mimic the squatting from some videos, but as I went down, I can only keep the knees right above the toes, is it okay? The knees tend to go forwards, but I can keep them back by focusing and downward movement in my butt.

2 Answers
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I recommend reading this article on the "Third World Squat". The general guidelines on position, etc. are good. Essentially it will help you gain the flexibility you will need in order to do any type of squat in safety.

Now, it is OK if the knees go a little bit forward. Acceptable is up to an inch in front of your toes. When you have a barbell on your back (assuming you will eventually do that), the idea is that the barbell will be positioned so that it is over your mid-foot. The only way to do that properly is to have the knees go up to an inch in front of your toes.

You do want to break parallel with your body weight squats (or any kind of squat for that matter). Parallel is defined as when the crease of your hips breaks the plane of the top of the knee. In short it is when the top of your leg is parallel to the ground, not the bottom. This will improve your flexibility as well as use more of your posterior chain (glutes, hamstrings, etc.) and less of your knees to raise back up. In fact, if you are feeling it in your knees you are probably shifting your weight too far forward.

Mark Rippetoe has a video where he is doing classroom instruction for the squat. What's important to pay attention to whether you plan to use a barbell or not is the diagram on the whiteboard and the body position during the squat.

Also, depending on your limb lengths, your knees may naturally need to be further ahead of your toes than other peoples'. If you have long tibias and femurs compared to your torso, your knees will likely end up out past your toes.
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user3085Jun 18 '12 at 2:38

What do you mean by "break parallel"? Do you mean stop at parallel or go past parallel?
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CasebashJun 18 '12 at 4:37

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You want the hips to break the plane of being parallel with the tops of the knees and the floor. You don't have to go all the way down till your butt hits your shoes. If all you can do initially is get to parallel, so be it. But you want to work towards going past even if only by a couple centimeters (or about an inch).
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Berin LoritschJun 18 '12 at 11:17

The advice to not let your knees track past your toes is, when I've heard it, specifically for loaded squats. In unloaded "air" squats, where you don't have a barbell or similar implement involved, I think it's okay to let your knees track past your toes.

Air squats are pretty safe if you avoid moving ballistically. You can move fast, but don't throw your body; stay in control. Don't bounce off your calves at the bottom. Don't let your knees buckle inwards. Stand up as straight as possible.